John Lewis, Debenhams and House of Fraser are being investigated over allegations of price fixing in relation to a leading brand of sports bra.

The Office of Fair Trading (OFT) has issued the three department stores, along with the Shock Absorber bra-maker, with a “statement of objections” that alleges they broke competition laws by all agreeing to set resale prices.

So-called “anti-competition” measures are illegal because they tend to keep prices artificially high for the benefit of the retailers, with customers losing out.

The OFT accuses lingerie maker DB Apparel of entering into nine separate anti-competitive agreements between 2008 and 2011, applying nationally and across a number of products in the Shock Absorber range, which amount to a “serious infringement of competition law”.

DBA’s Shock Absorber brand is already highly successful in the UK, with a share in the sports bra market of approximately 15 per cent during the period in question and having previously run marketing campaigns with tennis star Anna Kournikova.

“Resale price maintenance limits competition between retailers and can lead to consumers paying higher prices.”

She said the regulator would consider representations from the accused companies before making a ruling - expected by next March - on whether there had been a breach of competition law.

All four of the companies allegedly involved denied any wrongdoing.

DB Apparel said: “We reject any allegations by the OFT that we have entered into any agreement or understanding with retailers as to their retail prices of our products.

“We have been transparent with UK authorities since the beginning of this process and will continue to defend ourselves vigorously in this investigation.”

House of Fraser said: “We are confident that we have been operating within all laws and regulations and are very supportive of any initiative which ensures pricing policies are fair for our customers.”

A Debenhams statement said: “Debenhams disputes these provisional findings of the OFT, but is not in a position to comment further at this stage. The matter is being dealt with by its external lawyers.”

John Lewis said: “John Lewis always strives to operate within the law and comply with regulations.

“We are fully cooperating with the OFT and will respond in due course.”